Question 1062943
{{{ sin(x)*tan(x) - sin(x) + tan(x) - 1 = 0 }}}
{{{ sin(x)*( tan(x) - 1 ) + ( tan(x) - 1 ) = 0 }}}
{{{ ( sin(x) + 1 )*( tan(x) - 1 ) = 0 }}}
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either:
(1) {{{ sin(x) = -1 }}}
or
(2) {{{ tan(x) = 1 }}}
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For (1), 
{{{ x = 3*pi/2 }}}
For (2)
{{{ x = pi/4 }}}
{{{ x = 5*pi/4 }}}
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So, there are 3 answers in [ 0,2*pi]
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check:
{{{ sin(x)*tan(x) - sin(x) + tan(x) - 1 = 0 }}}
{{{ x = 3*pi/2 }}}
{{{ sin(3*pi/2)*tan(3*pi/2) - sin(3*pi/2) + tan(3*pi/2) - 1 = 0 }}}
{{{ (-1)*(1/0) - (-1) + 1/0 - 1 = 0 }}}
I don't think this can be determined. Thar leaves 2 answers
{{{ sin(x)*tan(x) - sin(x) + tan(x) - 1 = 0 }}}
{{{ sin(pi/4)*tan(pi/4) - sin(pi/4) + tan(pi/4) - 1 = 0 }}}
{{{ ( sqrt(2)/2 )*1 - sqrt(2)/2 + 1 - 1 = 0 }}}
{{{ 0 = 0 }}}
and, also:
{{{ sin(x)*tan(x) - sin(x) + tan(x) - 1 = 0 }}}
{{{ sin(5*pi/4)*tan(5*pi/4) - sin(5*pi/4) + tan(5*pi/4) - 1 = 0 }}}
{{{ (-sqrt(2)/2)*1 - (-sqrt(2)/2) + 1 - 1 = 0 }}}
{{{ 0 = 0 }}}
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{{{ x = pi/4 }}}
{{{ x = 5*pi/4 }}}
are the answers
get another opinion, definitely